#### 6.4.1 1.1

6.4.1.1 [1021] Example 1
6.4.1.2 [1022] Example 2
6.4.1.3 [1023] Example 3

##### 6.4.1.1 [1021] Example 1

problem number 1021

Chapter 4.1.1 example 1 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$

$w_x + a y w_y = b y^2 w$

Mathematica

$\left \{\left \{w(x,y)\to e^{\frac{b y^2}{2 a}} c_1\left (y e^{-a x}\right )\right \}\right \}$

Maple

$w \left ( x,y \right ) ={\it \_F1} \left ( y{{\rm e}^{-ax}} \right ){{\rm e}^{1/2\,{\frac{b{y}^{2}}{a}}}}$

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##### 6.4.1.2 [1022] Example 2

problem number 1022

Chapter 4.1.1 example 2 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$

$w_x + a y w_y = b e^{\lambda x} y w$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (y e^{-a x}\right ) e^{\frac{b y e^{\lambda x}}{a+\lambda }}\right \}\right \}$

Maple

$w \left ( x,y \right ) ={\it \_F1} \left ( y{{\rm e}^{-ax}} \right ){{\rm e}^{{\frac{by{{\rm e}^{\lambda \,x}}}{a+\lambda }}}}$

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##### 6.4.1.3 [1023] Example 3

problem number 1023

Chapter 4.1.1 example 3 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$

$w_x + a w_y = b w$

Mathematica

$\left \{\left \{w(x,y)\to e^{b x} c_1(y-a x)\right \}\right \}$

Maple

$w \left ( x,y \right ) ={\it \_F1} \left ( -ax+y \right ){{\rm e}^{bx}}$

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